Exploration of complex metal 2D design rules using inverse lithography

As design rule (DR) scaling continues to push lithographic imaging to higher numerical aperture (NA) and smaller k1 factor, extensive use of resolution enhancement techniques becomes a general practice. Use of these techniques not only adds considerable complexity to the design rules themselves, but also can lead to undesired and/or unanticipated problematic imaging effects known as "hotspots." This is particularly common for metal layers in interconnect patterning due to the many complex random and bidirectional (2D) patterns present in typical layout. In such situations, the validation of DR becomes challenging, and the ability to analyze large numbers of 2D layouts is paramount in generating a DR set that encodes all lithographic constraints to avoid hotspot formation. Process window (PW) and mask error enhancement factor (MEEF) are the two most important lithographic constraints in defining design rules. Traditionally, characterization of PW and MEEF by simulation has been carried out using discrete cut planes. For a complex 2D pattern or a large 2D layout, this approach is intractable, as the most likely location of the PW or MEEF hotspots often cannot be predicted empirically, and the use of large numbers of cut planes to ensure all hotspots are detected leads to excessive simulation time. In this paper, we present a novel approach to analyzing fullfield PW and MEEF using the inverse lithography technology (ILT) technique, [1] in the context of restrictive design rule development for the 32nm node. Using this technique, PW and MEEF are evaluated on every pixel within a design, thereby addressing the limitations of cut-plane approach while providing a complete view of lithographic performance. In addition, we have developed an analysis technique using color bitmaps that greatly facilitates visualization of PW and MEEF hotspots anywhere in the design and at an arbitrary level of resolution. We have employed the ILT technique to explore metal patterning options and their impact on 2D design rules. We show the utility of this technique to quickly screen specific rule and process choices-including illumination condition and process bias-using large numbers of parameterized structures. We further demonstrate how this technique can be used to ascertain the full 2D impact of these choices using carefully constructed regression suites based on standard random logic cells. The results of this study demonstrate how this simulation approach can greatly improve the accuracy and quality of 2D rules, while simultaneously accelerating learning cycles in the design phase.